This is where it gets fun! As a precursor, I'm a leftist that reads Marxist and Anarchist theory without dedicating to any specific tendency, as I feel that's an issue for when we are further down the line.

Alright, step 1. We've decided to reject individual ownership of Capital. How do we go about replacing this, with a functional system?

The Marxist-Leninists would say that we would need to build up a network of Worker councils that ladder upward, that way everyone can have direct influence on their local situations, and anyone who moves up the chain must do so from the bottom upward, creating a form of meritocracy. The state owns everything, and the state is of and for the Workers, creating democratically controlled production.

The Anarchists take issue with this as it lacks direct influence on the top from the bottom, and prefer more decentralization. In more Anarchistic models, typically complex webs of Communes practice Mutual Aid, and operate off of gift economies. FOSS is an excellent example of this in practice, in the real world! People contribute what they can and want to, and recieve what others are willing to give. It's a deceptively complex system to build, and isn't as simple as just blowing up the state, despite what TV will have you believe.

The Syndicalists have yet another view. They see revolutionary pressure from Unionization, and wish to see mass union strikes gain control of various industries. Then, following successful revolution, each industry will form a syndicate in a federated system.

The Market Socialists have again another view. They wish to have a market economy, but owned and operated via Worker Co-operatives and other such structures. Usually this is combined with Democratic Socialism, and structured similar to a liberal democracy (imagine America but with worker co-ops entirely).

The Council Communists are generally an anti-Stalin, pro-Marx, pro-Lenin Tendency that wish to see less centralization than in a Soviet Republic, and have Worker councils themselves own and run everything, without the same structure of laddering.

You can see that there are many, many, many different arguments for how to structure a leftist society, but all boil down to democratization of industry in different forms.